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Simplifying 3x((17 + -9x) + -1(16x + -10)) = 30 + -23x Remove parenthesis around (17 + -9x) 3x(17 + -9x + -1(16x + -10)) = 30 + -23x Reorder the terms: 3x(17 + -9x + -1(-10 + 16x)) = 30 + -23x 3x(17 + -9x + (-10 * -1 + 16x * -1)) = 30 + -23x 3x(17 + -9x + (10 + -16x)) = 30 + -23x Reorder the terms: 3x(17 + 10 + -9x + -16x) = 30 + -23x Combine like terms: 17 + 10 = 27 3x(27 + -9x + -16x) = 30 + -23x Combine like terms: -9x + -16x = -25x 3x(27 + -25x) = 30 + -23x (27 * 3x + -25x * 3x) = 30 + -23x (81x + -75x2) = 30 + -23x Solving 81x + -75x2 = 30 + -23x Solving for variable 'x'. Reorder the terms: -30 + 81x + 23x + -75x2 = 30 + -23x + -30 + 23x Combine like terms: 81x + 23x = 104x -30 + 104x + -75x2 = 30 + -23x + -30 + 23x Reorder the terms: -30 + 104x + -75x2 = 30 + -30 + -23x + 23x Combine like terms: 30 + -30 = 0 -30 + 104x + -75x2 = 0 + -23x + 23x -30 + 104x + -75x2 = -23x + 23x Combine like terms: -23x + 23x = 0 -30 + 104x + -75x2 = 0 Begin completing the square. Divide all terms by -75 the coefficient of the squared term: Divide each side by '-75'. 0.4 + -1.386666667x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.386666667x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.386666667x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.386666667x + x2 = 0 + -0.4 -1.386666667x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.386666667x + x2 = -0.4 The x term is -1.386666667x. Take half its coefficient (-0.6933333335). Square it (0.4807111113) and add it to both sides. Add '0.4807111113' to each side of the equation. -1.386666667x + 0.4807111113 + x2 = -0.4 + 0.4807111113 Reorder the terms: 0.4807111113 + -1.386666667x + x2 = -0.4 + 0.4807111113 Combine like terms: -0.4 + 0.4807111113 = 0.0807111113 0.4807111113 + -1.386666667x + x2 = 0.0807111113 Factor a perfect square on the left side: (x + -0.6933333335)(x + -0.6933333335) = 0.0807111113 Calculate the square root of the right side: 0.28409701 Break this problem into two subproblems by setting (x + -0.6933333335) equal to 0.28409701 and -0.28409701.Subproblem 1
x + -0.6933333335 = 0.28409701 Simplifying x + -0.6933333335 = 0.28409701 Reorder the terms: -0.6933333335 + x = 0.28409701 Solving -0.6933333335 + x = 0.28409701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6933333335' to each side of the equation. -0.6933333335 + 0.6933333335 + x = 0.28409701 + 0.6933333335 Combine like terms: -0.6933333335 + 0.6933333335 = 0.0000000000 0.0000000000 + x = 0.28409701 + 0.6933333335 x = 0.28409701 + 0.6933333335 Combine like terms: 0.28409701 + 0.6933333335 = 0.9774303435 x = 0.9774303435 Simplifying x = 0.9774303435Subproblem 2
x + -0.6933333335 = -0.28409701 Simplifying x + -0.6933333335 = -0.28409701 Reorder the terms: -0.6933333335 + x = -0.28409701 Solving -0.6933333335 + x = -0.28409701 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6933333335' to each side of the equation. -0.6933333335 + 0.6933333335 + x = -0.28409701 + 0.6933333335 Combine like terms: -0.6933333335 + 0.6933333335 = 0.0000000000 0.0000000000 + x = -0.28409701 + 0.6933333335 x = -0.28409701 + 0.6933333335 Combine like terms: -0.28409701 + 0.6933333335 = 0.4092363235 x = 0.4092363235 Simplifying x = 0.4092363235Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9774303435, 0.4092363235}
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